多项式微分方程的广义反射函数及其周期解  

Generalized Reflective Function and Periodic Solution of Polynomial Differential Equation

作　　者：潘颖昕[1] 高巧萍[1] 刘文俊[2] 

机构地区：[1]如皋高等师范学校数理与信息技术系,江苏如皋226500 [2]扬州大学数学科学学院,江苏扬州225002

出　　处：《淮海工学院学报（自然科学版）》2014年第2期11-13,共3页Journal of Huaihai Institute of Technology:Natural Sciences Edition

基　　金：江苏省高等学校大学生实践创新训练计划资助项目(201311117084X)

摘　　要：为了研究多项式微分方程周期解的存在性与稳定性,通过多项式微分方程的广义反射函数来寻找其Poincaré映射.给出了多项式微分方程具有线性广义反射函数的充要条件,以及在该条件下线性广义反射函数的具体表达式和多项式微分方程周期解的存在性与稳定性.该结果对研究相关微分方程周期解与稳定性具有一定的参考价值和指导意义.In order to study the problem associated with periodic solution and stability of polyno-mial differential equation,this paper proposes a method to find its Poincare mapping through polynomial differential equation’s generalized reflective function.It establishes the necessary and sufficient conditions for polynoe genermial differential equation to have linear generalized reflective function.Under these conditions the form of thalized reflective function has been established and the existence and stability of the periodic solution has been discussed.This study is of reference and guiding value for researches on the periodic solution and the stability of other differential equations.

关 键 词：多项式微分方程 广义反射函数 周期解 

分 类 号：O175.14[理学—数学]